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# In the Land of Oz only one or two-letter words are used. The

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In the Land of Oz only one or two-letter words are used. The [#permalink]  02 Jun 2012, 02:38
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14% (00:00) correct 85% (00:39) wrong based on 0 sessions
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132
[Reveal] Spoiler: OA
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Re: In the Land of Oz only one or two-letter words [#permalink]  02 Jun 2012, 03:42
I am getting the answer as 131 - D

Earlier there were 66 letters
No of two letter words = 66*65
Single letter word = 66
Total = 66^2

Now there were 65 letters
No of two letter words = 65*64
Single letter word = 65
Total = 65^2

Diff = 66^2 - 65^2 = 131 = lost words
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Re: In the Land of Oz only one or two-letter words [#permalink]  02 Jun 2012, 03:46
Alternate solution

The seventh letter (Let it be @) can be used with other 65 in two type of arrangents
one when seventh letter is in 1st slot @_ (65 ways)
another, when seventh letter is in 2nd slot _@ (65 ways)

seventh letter (@) itself

Lost words = 1 + 65 + 65 = 131
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Re: In the Land of Oz only one or two-letter words [#permalink]  02 Jun 2012, 04:19
Number of one letter words that can be made using 66 letters = 66
Number of two letter words that can be made using 66 letters = 66C2*2!
Total number of words using all 66 letters = 66 + 66C2 * 2!

Number of one letter words that can be made using 65 letters = 65
Number of two letter words that can be made using 65 letters = 65C2*2!
Total number of words using 65 letters = 65 + 65C2*2!

Number of words that the language has lost = 66 + 66C2*2! - (65+65C2*2!)
= 1 + 130
= 131

Choice D
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Re: In the Land of Oz only one or two-letter words [#permalink]  02 Jun 2012, 04:24
GyanOne wrote:
Number of one letter words that can be made using 66 letters = 66
Number of two letter words that can be made using 66 letters = 66C2*2!
Total number of words using all 66 letters = 66 + 66C2 * 2!

Number of one letter words that can be made using 65 letters = 65
Number of two letter words that can be made using 65 letters = 65C2*2!
Total number of words using 65 letters = 65 + 65C2*2!

Number of words that the language has lost = 66 + 66C2*2! - (65+65C2*2!)
= 1 + 130
= 131

Choice D

official answer is Definitely E , I have rechecked . Let's wait for expert solution.

Mean while please tell me how you got the total number of 2 letter words , Permutation tells me (66!)/(64!) which gives me 66*65 . But I can't figure out 65C2*2!
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Re: In the Land of Oz only one or two-letter words are used. The [#permalink]  02 Jun 2012, 06:36
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In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Hope it's clear.
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Re: In the Land of Oz only one or two-letter words are used. The [#permalink]  02 Jun 2012, 07:18
Bunuel on target as always
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Re: In the Land of Oz only one or two-letter words are used. The [#permalink]  02 Jun 2012, 07:25
Bunuel wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Hope it's clear.

+1 awesome , solution
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Re: In the Land of Oz only one or two-letter words are used. The [#permalink]  02 Jun 2012, 19:24
Bunuel wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Hope it's clear.

silly mistakes as ever.....
Thanks Bunuel
Re: In the Land of Oz only one or two-letter words are used. The   [#permalink] 02 Jun 2012, 19:24
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